高等学校数学Ａ 「条件付き確率」 の導入場面の教材と授業
2023 年 29 巻 1 号 p. 69-83
詳細
2023 年 29 巻 1 号 p. 69-83
The probability we consider in our daily lives is conditional probability. For this reason, the teaching of conditional probability is important in school mathematics. However, some problems have been pointed out in teaching conditional probability. For example, although previous researches have pointed out the problems of tasks and lessons for the introduction of conditional probability, they have not led to the design and verification of specific tasks and lessons. Therefore, the purpose of this paper is to design and verify tasks and lessons for the introduction of conditional probability in school mathematics. The theoretical framework is the process of formulating the concept of conditional probability from the perspective of negation.
As a result, we first identified the hypotheses about tasks and classes. The hypotheses about tasks are: “If we use a question that asks for the probability of cause, which is the opposite of the probability of outcome, as an introductory question to conditional probability, students may realize that they cannot derive an appropriate model given the information they have”, and “If the question involves several people with different information about the same event, students may realize that probabilities apply to our information about the event”. The hypothesis about the lessons is that ［1］ students recognize that using unconditional probability, students recognize that they cannot derive an appropriate model in consideration of the information obtained, ［2］ they reinterpret the probability that does not ignore the condition as conditional probability, and ［3］ they avoid confusing unconditional and conditional probability by characterizing the former as a model that has no conditions related to the event. This course of instruction is effective as an introduction for students to formulate the concept of conditional probability. We then designed and implemented a task and a lesson to illustrate these hypotheses, targeting 10th grade students who had not studied conditional probability. As a result, we were able to illustrate three hypotheses.
